Lifting surfaces (wings) create drag when they create lift. This drag-due-to-lift is called “induced drag.” A significant portion of the induced drag is attributed to the magnitude of the vortex induced at the tip of each wing. Over the years many devices have been proposed to reduce the strength of this tip vortex. Winglets, which are small lift generating surfaces placed at the tip of each wing, if designed properly, have been shown to significantly reduce this tip vortex thereby reducing the wing's induced drag.
The basic design and operational effectiveness of “winglets” is described in “A Design Approach and Selected Wind-Tunnel Results at High Subsonic Speeds For Wing-Tip Mounted Winglets”, by Richard T. Whitcomb, NASA Technical Note TN D-8260, July, 1976. Some of the subsequent winglet construction designs in the patent literature are disclosed by U.S. patents: U.S. Pat. No. 4,017,041, granted Apr. 12, 1977 to Wilbur C. Nelson; U.S. Pat. No. 4,190,219, granted Feb. 26, 1980, to James E. Hackett; U.S. Pat. No. 4,205,810, granted Jun. 3, 1980, to Kichio K. Ishimitsu; U.S. Pat. No. 4,240,597, granted Dec. 23, 1990, to Roger R. Ellis, W. Martin Gertsen and Norman E. Conley; U.S. Pat. No. 4,245,804, granted Jan. 20, 1981, to Kichio K. Ishimitsu and Neal R. Van Devender; U.S. Pat. No. 4,714,215, granted Dec. 22, 1987, to Jeffrey A. Jupp and Peter H. Rees; U.S. Pat. No. 5,275,358, granted Jan. 4, 1994 to Mark I. Goldhammer and Karela Schippers; U.S. Pat. No. 5,348,253, granted Sep. 20, 1994 to Louis B. Gratzer; U.S. Pat. No. 5,407,153, granted Apr. 18, 1995 to Philip S. Kirk and Richard Whitcomb; U.S. Pat. No. 6,484,986 B2, granted Nov. 26, 2002 to Fort F. Felker; and U.S. Pat. No. 6,722,615 B2, granted Apr. 20, 2004 to Cierd Heller and Peter Kreuzer. A novel design having fully curved spiroidal shaped wing tip is presented in U.S. Pat. No. 5,102,068 granted Apr. 7, 1992 to Louis B. Gratzer.
FIGS. 1-7 reflect prior art concepts as shown in several of the above prior U.S. patents. FIGS. 1-4 reflect the disclosure in U.S. Pat. No. 5,275,358 (the “'358 patent”). Referring to FIG. 1, showing an entire aircraft (2) provides basic orientation for the terminology used herein. The aircraft basically comprises an aircraft body (4), left and right wings (6, 6A), and a tail section (8). A winglet (10, 110) is shown at the outer end of each wing (6). A fuselage coordinate system (X, Y, Z) is defined for the aircraft (2) in the following manner. A longitudinal axis (X) is defined to extend through the center of the aircraft body (4) in the fore and aft directions. Further, a vertical axis (Z) is defined in the up and down directions, while a transverse axis (Y) is defined in the left and right directions. The longitudinal axis (X), vertical axis (Z) and transverse axis (Y) are orthogonal to each other and meet at an origin located at the foremost plane of the aircraft (2).
A wing coordinate system (x, y, z) is defined wherein the wing coordinate system x axis is coincident with a reference wing chord, generally at the wing inner or root location, the wing coordinate system x axis being at an angle, alpha, about the fuselage Y axis from the fuselage coordinate system X-Y plane, said angle, alpha, defining the wing angle of incidence (note for wings incorporating airfoil section twist, the angle if incidence varies with wing span location along the wing coordinate system y axis), the wing coordinate system y axis is located at the forward end of the reference wing chord and is normal to the wing coordinate system x axis and at an angle, epsilon, about the fuselage coordinate system X axis from the fuselage coordinate system X-Y plane, said angle, epsilon, defining the wing dihedral angle, the wing coordinate system x-y plane defining a wing reference plane, the wing coordinate system z axis is normal to the wing coordinate system x-y plane.
Referring to FIGS. 2 and 3, a winglet (10) (from the right wing of the aircraft), which is generally composed of an upper sail or trapezoidal shape (16) and a lower transition shape (33), is joined to the wingtip (12) so that the winglet (10) extends outwardly and upwardly from the wingtip (12). The wingtip (12) (FIG. 2) has upper and lower wing surfaces (18) and (20), a wing leading edge (22), and a wing trailing edge (24). Similarly, the winglet (10) has upper and lower winglet surfaces (26) and (28), a winglet leading edge (30), a winglet trailing edge (32), and a wing/winglet intersection (14). Conventionally, the terms “upper” and “lower” used in reference to the winglet (10) generally corresponds to the “inner” and “outer” directions, respectively. This convention will be followed herein. The winglet (10) is generally described as having a lower transition section (33), adjacent to the wingtip region, and an upper sail or trapezoidal shaped section (34), distal from the wing. The leading edge (30) of the sail or trapezoidal section (34) is swept back at an angle (35) from the vertical z-axis. The sail section (34) is also canted at angle phi (36) from a plane parallel to the (x) and (z) axis (FIG. 3).
FIG. 4 is another example of the prior art and exemplifies an invention of the '358 patent. Here, the wing tip region is designated (112). Line (114) is where the wing reference plane (148) intersects the winglet upper or sail section reference plane (150). The wing (112) has upper and lower wing surfaces (118 and 120), a wing leading edge (122), a wing trailing edge and a wing root (not shown). The winglet (116) extends outboard and upward from the wing tip (112). The winglet (116) has upper and lower winglet surfaces (126 and 128), a winglet leading edge (130), a winglet trailing edge, a winglet root, and a winglet tip.
FIG. 5 is another example of the prior art and exemplifies an invention of the '253 patent and presents what is referred to as a “blended winglet”, wherein the winglet profile is made up of an arc-line curve. Referring to FIG. 5, the winglet chord equals the wing tip chord at the attachment line (3). A winglet transition section (2) is bounded by the transition line (3) and a chordwise line (4) designating the transition end of the winglet (9). The nearly planar (slightly non-planar due to airfoil twist distribution) upper or sail portion of the winglet (9) has straight line profile from the transition end (4) to the tip (5). A feature of the FIG. 5 wing/winglet arrangement is a continuous monotonic chord variation bounded by a leading edge curve (7) and a trailing edge curve (8). These curves are tangent to the wing leading edge and trailing edge respectively at the winglet attachment line (3) and are also tangent to the leading edge and trailing edges respectively of the straight section (9) at line (4). The leading edge curve (7) is selected to provide a smooth gradual chord variation in the transition and also, to limit the leading edge sweep angle to less than about 65 degree. According to U.S. Pat. No. 5,348,253 this is necessary to avoid vortex shedding from the leading edge which would compromise the surface loading and thereby increase drag. The shape of the leading edge curve (7) is generally not critical but is selected to correspond to the airfoil chord and twist required to achieve optimum loading.
U.S. Pat. No. 5,348,253 also discloses that the rate of curvature R must be large enough to accommodate a continuous monotonic variation of cant angle in the transition section in order to allow the practical achievement of optimum aerodynamic loading and minimum interference between wing and winglet. The radius and curvature criteria is given by U.S. Pat. No. 5,348,253 and repeated below in terms of a parameter, Kr, having fairly narrow limits.R/h=Kr*cos(phi/2+pi/4)/cos(phi)
where;
Kr=curvature parameter, where 0.35<Kr<0.5 (select lower limit if practical)
h=winglet height (normal to wing ref plane)
phi=cant angle of planar sail section 0<phi<40, and 140<phi<180
pi=3.14159
R=blend section (adjacent the wingtip section) radius
From the above equation, the curvature parameter Kr used in U.S. Pat. No. 5,348,253 is the ratio of the winglet arc section span increase (R*cos(phi)) to the length of the projection of the winglet height (as viewed in the wing yz plane) onto a plane rotated at an angle of (phi+90)/2 about the winglet tip. As shown in FIG. 6A, the length of this projection is h*cos((phi+90)/2), thus Kr=R*cos(phi)/(phi)/(h*cos((phi+90)/2)). More details regarding the arc-line blended winglet design are set forth in U.S. Pat. No. 5,348,253. The radius and curvature criteria as given by U.S. Pat. No. 5,348,253 and repeated here, shows that Kr was arbitrarily selected and has fairly narrow limits. Furthermore, when viewing all of these concepts, both for the prior art and for the present invention, that aircraft wings have a certain handedness, such that when discussing these issues it must be taken into account whether one is dealing with the left wing and left winglet, or the right wing and right winglet.
FIG. 6 is another example of the prior art and exemplifies an invention of the '253 patent. FIG. 6 depicts an embodiment of an elliptical profile winglet. Here, the outer end of the wing (200) meets the inner end of the winglet (202) at intersection (204). The major axis (206) of an ellipse is shown to extend perpendicular to the wing reference plane and to coincide with the intersection (204). The minor axis (208) of the ellipse extends perpendicular to the major axis and intersects the major axis at center (210). If one were to draw a diagonal line (212) from the center (210) to the outer end or tip (214) of the winglet (202), an acute angle (216) would be defined between the line (212) and the major axis (206). In FIG. 6, the dihedral angle of the wing (200) is designated (218). The winglet height is designated (220) and the winglet span is designated (222). The wing tip cant angle is designated (224). According to the invention, the winglet (202) curves upwardly and outwardly from intersection (204) to the outer end or tip (214) of the winglet (202).
U.S. Pat. No. 5,348,253 states that the winglet profile could be any continuous conic section with the winglet (202) preferably having a curvature in the y-z plane that at least approximates a sector of an ellipse measured from intersection station (204) outwardly to the winglet outer end or tip (214). At intersection station (204), the curvature of the winglet surfaces meets the wing surfaces substantially at a tangent. As the winglet (202) extends outwardly from the intersection station (204), its curvature in the y-z plane changes in substantially the same way that an elliptical surface changes